In a control engineering sense AI (or in this case learning based approaches) and classical control based approaches are just different sides of the same coin.
In control theory the problem is to control a system (sometimes called the plant) to behave in a desired way. The desired way is given (in form of a reference value, which can change over time).
The simplest form of closed loop control is to take the current, measured value subtract this from the reference value and the error signal is created. This difference is the beginning of any closed loop control. Simplest is to multiply this with a constant to make sure that if there is an error between these two the system will try to "move" in order to get to the reference value.
There are many advanced and complicated approaches to achieve this. Simplest above is the P (proportional) controller but one can complicate this further with integrative and derivative terms and end up with the so called PID controller (still the most used in industrial practice). Control systems have evolved and model based predictive, optimal etc. control approaches have been developed.
However, the control problem can be formulated as a machine learning problem and this is how machine learning can be mixed with control theory. Probably one of the fundamentally new approaches is the PILCO approach presented here.
So.. for low level control learning and classical control is somewhat interchangeable. (Machine learning based control systems can behave fully deterministically after training)
In higher levels closed loop control has sometimes been used, but mostly, for robots planning methods generate paths to be followed by the closed loop controllers. These paths can be hard-coded like in the case of most industrial robots or more flexibly defined as in the case of service robots. Planning problems and their solutions have always been a subfield of AI, therefore it can be argued that any robot which solves a planning problem is AI-based. Machine learning itself is also a subfield of AI. Machine learning methods can also solve planning problems.
If we take grasping as an example.
Detecting grasp point can be done using classical machine vision, with no machine learning or with a neural network based approach e.g. 2. These methods are interchangeable ans dome perform better then the others in different situation.
Any robot which ever navigated a labyrinth is AI-based. Way-finding in a labyrinth is a classical AI planning problem. Somewhat novel are the machine learning based solutions for these well known planing problems.
In areas such as speech recognition or gesture recognition is a similar situation. These have been always part of AI, the novelty, also here is the success of machine learning based approaches. Here again, methods, classical vs. machine learning based are interchangeable, but the latter have a much better success for these applications.